This result is the same as (1.7a) in ref.[1]} (horizon radius \(r_H=1\) ). We extend pole-skipping phenomenon at higher Matsubara frequencies \(\omega _n=-i2\pi Tn\) , and the method has been showed in section . We expand the \(\chi (r)\)  with a Taylor series
\(\chi (r)=\sum ^\infty _{p=0}\chi _p(r-r_H)^p=\chi _0+\chi _1(r-r_H)+\dots .\) 
